Real Life Applications of Tessellations

Tessellations can be found in many areas of life. Art, architecture, hobbies, and many other areas hold examples of tessellations found in our everyday surroundings. Specific examples include oriental carpets, quilts, origami, Islamic architecture, and the are of M. C. Escher.

Oriental carpets hold tessellations indirectly. Although they aren’t often in the field pattern of the carpet or rug, you may find them in the borders of the rugs. Also, any two dimensional pattern has an underlying grid structure that is made up o f tessellations. Also, quilt patterns many times have tessellations that can be found in them, as shown in this Lady of the Lake quilt pattern.

http://web.inter.nl.net/hcc/Hans.Kuiper/quilt02.htm

Islamic Architecture is a good place to find tessellations. Architects could not depict any animals or humans on any buildings because people thought this might lead to idol worship. So, Islamic art utilized geometric, floral, arabesque, and callig raphic primary forms, which are often interwoven into the architecture.

Tessellations can be found in the hobby or art of origami. Back in the 1970’s Shuzo Fujimoto gave birth to folding paper into tessellations. Paper is folded into triangles, hexagons, and squares to form many different patterns and shapes.

This tessellation is called the honeycomb, another place to find tessellations in the real world. Another hobby of sorts are puzzles. There are puzzles on the market that you can manipulate different shapes and make your ow n tessellations out of those.


The art of M.C. Escher is used extensively in the realm of tessellations. Escher calls his paintings like this divisions of the plane and even went as far as to make up his own classifications system of the plane divisions. He often divides the plane with animal figures as shown in the Fish and Boats. This drawing was used in a 1949 New Year’s greeting card that he had been asked to complete.

http://lonestar.texas.net/~escher/gallery/Fish&Boats.html

One of the best examples of tessellations in Escher’s paintings is Lizards:


http://lonestar.texas.net/~escher/gallery/Lizards.html

This painting repeats the same six sided figure in sets of three over and over. Escher was not trained formally in any mathematics and yet was fascinated by what he found. He once said, "The regular division of the plane into congruent figures evoking an association in the observer with a famili ar natural object is one of these hobbies or problems...I have embarked on this geometric problem again and again over the years, trying to throw light on different aspects each time. I cannot imagine what my life would be like if this problem had never o ccurred to me; one might say that I am head over heels in love with it, and I still don’t know why." Mathematicians, scientists and crystallographers all appreciate his work, and some of his prints have been used to study visual perception in fields like physics, geology, chemistry, and psychology. The print to best illustrate this is Sky and Water I in which birds and fish are used t o tessellate the plane.


http://lonestar.texas.net/~escher/gallery/Sky&Water.html

So, there are many real life applications for tessellations. Hobbies, art, architecture, and carpets are only a few of the places that tessellations can be found in our world.

 

 

References

http://www.sanger.ac.uk/~agb/Origami/Tessellation/tessellation1.html"

http://web.inter.nl.net/hcc/Hans.Kuiper/quilt02.htm

http://lonestar.texas.net/~escher/

http://www.ced.berkeley.edu/~irydhan/islamarc.html